Taiwanese Journal of Mathematics

$\mathcal{C}^{1}$ SELF-MAPS ON $\mathbb{S}^{n}$, $\mathbb{S}^{n}\times \mathbb{S}^{m}$, $\mathbb{C}$P$^{n}$ AND $\mathbb{H}$P$^{n}$ WITH ALL THEIR PERIODIC ORBITS HYPERBOLIC

Juan Luis García Guirao and Jaume Llibre

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We study in its homological class the periodic structure of the $\mathcal{C}^{1}$ self$-$maps on the manifolds $\mathbb{S}^{n}$ (the $n-$dimensional sphere), $\mathbb{S}^{n}\times \mathbb{S}^{m}$ (the product space of the $n-$dimensional with the $m-$dimensional spheres), $\mathbb{C}$P$^{n}$ (the $n-$dimensional complex projective space) and $\mathbb{H}$P$^{n}$ (the $n-$dimensional quaternion projective space), having all their periodic orbits hyperbolic.

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Taiwanese J. Math., Volume 16, Number 1 (2012), 323-334.

First available in Project Euclid: 18 July 2017

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Primary: 37C05: Smooth mappings and diffeomorphisms 37C25: Fixed points, periodic points, fixed-point index theory 37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems

hyperbolic periodic point period Lefschetz zeta function Lefschetz number sphere complex projective space quaternion projective space


García Guirao, Juan Luis; Llibre, Jaume. $\mathcal{C}^{1}$ SELF-MAPS ON $\mathbb{S}^{n}$, $\mathbb{S}^{n}\times \mathbb{S}^{m}$, $\mathbb{C}$P$^{n}$ AND $\mathbb{H}$P$^{n}$ WITH ALL THEIR PERIODIC ORBITS HYPERBOLIC. Taiwanese J. Math. 16 (2012), no. 1, 323--334. doi:10.11650/twjm/1500406543. https://projecteuclid.org/euclid.twjm/1500406543

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